Estimation and Evaluation the Reliability of Production Machines Practical Study of the Textile Department/the National Establishment of the Jordanian Textiles in the Industrial King

Procedia - Social and Behavioral Sciences 93 ( 2013 ) 125 – 133

1877-0428 © 2013 The Authors. Published by Elsevier Ltd.Selection and peer review under responsibility of Prof. Dr. Ferhan Odabaşıdoi: 10.1016/j.sbspro.2013.09.164

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3rd World Conference on Learning, Teaching and Educational Leadership (WCLTA-2012)

Estimation and evaluation the reliability of production machines Practical Study of the Textile Department / the National Establishment of the Jordanian

Textiles in the Industrial King Abdullah II City

Hasan Touama, Mazen Basha* Association Professor in Statistics, Faculty of Economics and Administrative Science , Zarqa University, Jordan

Abstract

The most eminent results of technical revolution are the appearance of many electronic equipments and complicated tools. These equipments and tools are mostly vulnerable to breakdown or (technical failure). Therefore the reliability measurement of any equipment should be important base for development of most equipment and tools. The reliability is a probability and statistical concept to be used in analyzing random variables of positive values represented by time (T) until (time–to–failure) of any equipment. The research aim consists of applying the parametric methods for estimation the reliability of tool productivity of textile department in the Jordanian Textiles in King Abdullah II Industrial City. The study results shows that the reliability of machines were low, which indicates that the establishment management should re-evaluate the productive activities thereof.

© 2012 Published by Elsevier Ltd. Selection and peer review under the responsibility of Prof. Dr. Ferhan Odabaşı

Keywords: Reliability, exponential distribution, maximum likelihood estimation, production machines. 1. Introduction

The productive operation in any organization is based on a certain set of essential inputs (productive

machines, workers and raw materials…). The productive machines are the most important part thereof, it is doubtless that these machines or any part thereof are vulnerable to breakdown or (technical failure), which leads to materialistic loss and waste of time beside other damages.

Thereupon, reliability evaluation of any machine must be an important base of these machines; for the reliability knowledge of each machine takes us, at the end of that, towards the proper planning of improvement and increase of (quality, productivity and efficiency of maintenance programs and productivity age), so as to produce products and services of high reliability, in harmony with the expectations and needs of the consumer which realizes the competitive advantage of the organization.

In order to show the role of the productive machines reliability and the importance thereon in textile section, the study had dealt with the employment of the laboratory ways in productive machines reliability in textile section of one *Mazen Hasan Basha. Tel.: +0-962-796198031 E-mail address: [email protected]

Available online at www.sciencedirect.com

© 2013 The Authors. Published by Elsevier Ltd.Selection and peer review under responsibility of Prof. Dr. Ferhan Odabaşı

126 Hasan Touama and Mazen Basha / Procedia - Social and Behavioral Sciences 93 ( 2013 ) 125 – 133

of our productive organizations which is represented with the national establishment of the Jordanian textile in King Abdulla II Industrial City, the study used (MLE) method to estimate the productive machines reliability for the eminent importance of the textile industry on both civil and military levels, preparing for establishment of correct scientific bases for textile industry in the kingdom which had been included in the different international treaties as the free commerce treaty with the European states and the Arab Protocols.

The reliability is a probabilistic and statistics term used to analyzing the random variables of the positive values and represented with time (T) until (Time to Failure) for any machine (equipment) takes place.

Therefore, the reliability throughout (t), is defined by the potentiality of the machine (equipment) during the period (0, t) without any breakdown (failure). 2. Methodology 2.1. Study problem

The entrance of the Hashemite Kingdom of Jordan in the different International treaties, as Free Commercial Treaty with European States and the Arab Protocol, has been reflected on our national institutions performance, which lead to the fact that what had been produced did not find its way to marketing, the thing which caused the decrease sales of the studied institution as an example without being exclusive by 80 % for the year 1998, because of the activation of the Arab protocol and the competition of the Arab product to the Jordanian product from one side, and our productive organization at present faces a case of prescription in the essential industrial and technological modernization operation on the second side, thereupon, the modern scientific bases for the ability of survival. Or ending of certain kinds of machines should be set, i.e. the formation of the industrial and technological base in the way of starting with scientific computation operation of reliability of each kind of machines rate, and each organization of our productive organization, and pursuance of the aforesaid ideas, the study problem could be briefed as follows: a. There exist a case of modernization and development of the essential and technological base in the National

Textile Jordanian Institution in the industrial city of King Abdulla II, for plenty of productive machines face a condition of economical extinction resulting from the international development of technology.

b. Lack of the operation scientific approach use to estimation the reliability of the productive machines in them aforesaid textile institution.

2.2. Study object

The object of the study comprises the employment of Parametric Method in general and Reliability in specific in the field of the estimation the reliability of the productive machines of the textile section in the Jordanian national institution, aiming at qualified programmer designing for productive machines maintenance in order to improvement of reliability thereof and facing all the conditions of the economical extinction, which makes the financial loses at its lower level. 2.3. Study hypotheses

The study hypotheses are given as follows: a. The machines work times between failures, for each machine of the textile section follows the exponential distribution with its parameter )(θ i.e. :

)exp(~t:H0 θ

)exp(~t:H1 θ/


b. There is no statistically a significance differences between the estimated values of reliability functions

)t(R̂i of the textile machines section which are to be studied, i.e.: H0: R1(t) = R2(t) = R3(t) = ….. = Ri(t) H1: At least two of the reliability functions are different. 3. Theoretical part 3.1. Reliability function R(t)

The reliability function is defined from the two sides ( the statistically and probability) as follows: If the random variable )0T( ≥ represents (time-to-failure) takes place, and it has a function of density

probability )t(f and the reliability of the equipment through out )t( is )t(R which takes the following formula (Smith 1976):

∫

∫

∞−

∞

−=

=

>=

t

t

du)u(f1

du)u(f

)tT(p)t(R

… (1)

Generally, the Reliability function )t(R is a decreasing function continuing from left within the period

),0[ ∞ , and this means that every equipment should be vanquished through out a certain temporal period (Johnson & Christensen, 1988). 3.2. Failure Rate Function )(tr

It is the ratio of the failed units through a certain temporal period to that period which remained till time )t( ,

the failure rate function )t(r takes the following formula ( Kapur & Laberson,1977).

3.3. Estimati

on the

Parameter and . Estimation the Parameter of the Exponential Distribution 3.3. Estimation the parameter and the reliability function of the exponential distribution

The probability density function )t(f of the machines time works of the textile section work till that occurrence of failure is distributed as exponential distribution and takes the following formula (Michael, 1991).

… (2)

)()(

)()(

1)(

tRtf

dttdR

tRtr

=

⋅−

=


0t,e1)t(ft

>⋅θ

= θ−

. ( ... 3)

Whereas: θ : Scale parameter, and defined that it is the (Mean Time Between Failure -MTBF)

This part deals with using the Maximum Likelihood Estimation Method (MLE) in estimation of the parameter )(θ and reliability function )t(R of the exponential distribution, as follows:

3.3.1. Estimation the Parameter of the Exponential Distribution

Throughout the Maximum Likelihood Estimation Method (MLE), we can get a frank formula for the estimator of the exponential distribution parameter )(θ , and in supposition of the fact that the random variable

)0T( ≥ has the probability density function )t(f as in the relation (3) , the function of the maximum

likelihood estimation of the random variables ( )n21 t...,,t,t is written as follows ( Pollock & Conroy, 1989):

∑⋅

θ=θ

θ−

n

iit1

n e1);t(L

Thereupon the estimator of maximum likelihood of the parameter )(θ is:

tn

tn

ii

==θ∑∧

....(4)

The above estimator )ˆ(θ is unbiased estimator of the parameter )(θ i.e.:

θ=θ)ˆ(E

The variable )( ∑=n

itiY is considered to be sufficient statistic for the parameter )(θ , and it is complete

sufficient statistic.

Whereas )ˆ(θ is considered as to be a function in the sufficient statistic )tiY(n

i∑= , Thereupon )ˆ(θ has

a minimum variance unbiased estimator (MVUE) of parameter )(θ .

3.3.2. Estimated the Reliability Function )t(R and Failure Rate Function )(tr

3.3.2.1. Estimated the Reliability Function )t(R

The reliability function )t(R of the machine work times which is distributed as exponential distribution, takes the following formula:

0t,e)t(Rt

>= θ−


Thereupon, the maximum likelihood estimator of the reliability function )t(R could be gotten after the

substitution of the value )ˆ(θ in the reliability function )t(R mentioned in the relation No. (5) as follows (Sinha & Kale 1980).

0t,e)t(R̂t

>= θ−

....( 5)

The above estimator )t(R̂ of the reliability function )t(R is considered to be a biased estimator, and

considering the variable )tY(n

ii∑= is sufficient statistic for the parameter )(θ and has complete sufficient

statistic, and by the theory (Lehmann & Sheffe), we can get the unbiased estimator of the reliability function

)t(R̂ as follows (Mook, Graybill & Boes, 1974):

0t,ti

11)t(R̂

1n

n

i

>

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

−=

−

∑ ....(6)

The above estimator )t(R̂ has a minimum variance unbiased estimator (MVUE) of the reliability function

)t(R .

3.3.2.2. Estimated the Failure Rate Function )(tr

The failure rate function )t(r , which considered a constant value of the exponential distribution takes the following formula:

θ=

1)t(r

Thereupon, the maximum likelihood estimator of the function )t(r is written as follows:

∑=

θ=

n

iit

nˆ1)t(r̂

....(7)

The estimator )t(r̂ mentioned in the relation (7) is considered a biased estimator, whereas the unbiased

estimator of the failure rate function )t(r̂ is written as follows:


∑

−= n

iit

1n)t(r̂ ....(8)

The above mentioned of failure rate function )t(r̂ has a minimum variance unbiased estimator (MVUE) for

the function )t(r . 4. Practical part 4.1. Collection data method

For the purpose of the Study, a great number of the textile section machines in the National Establishment of the Jordanian Textiles and used for performance of the suggested models for production by the design section in the establishment.

The concern was concentrated on the study of the three kinds of machines, for being shared in the production year 1985 and from different countries [Winder (20) machines, Sewing (16) machines and Twisting (12) machines], the other machines were excluded from the study because of the difference of the production year.

The required kinds of machines for study, a random sample were withdrawn at a percentage of (50%) for each type of machines as follows [Winder (10) machines, Sewing (8) machines and Twisting (6) machines].

Thereafter, the actual times for the three machines work to be studied was registered, till the damage breakdown occurrence, for the period (1/5/2011 – 1/11/2011), where the machine damage should be repaired and return for work.

4.2. Data analysis and the results discussions 4.2.1. The goodness of fit test of the machines work times

To test the goodness of fit of the machines work times data of each machine till the breakdown occurrence for testing the hypothesis saying (that the work time data of the machines between a failure and another failure, and for each machine of the textile section machines to be studied follow the exponential distribution with parameter thereof )(θ , where the mean time between failure (MTBF) for each machine was deduced depending on the relation No.(4), as shown in table (1) as follows:

Table 1. The (MTBF) of the machines

No. Machine ∧

θ= iMTBF

1 Winder 38.75

2 Sewing 43.14

3 Twisting 48.71

Thereupon the value of chi-square )( 2χ of the three machines are shown in table (2) as follows:


Table 2. The Chi-square )( 2χ of the machines

No.

Machine

2.calχ

df. ( )01.0,5

2χ

1 Winder 1.238 5 2 Sewing 1.093 5 15.09 3 Twisting 0.595 5

By comparing the calculated value ( 2.calχ ) in table (2) for all the machines which are to be studied with it's

tabulated value at the significant level (0.01), it appears that all calculated value ( 2.calχ ) is less than the tabulated

value amounting to (15.09), thereupon the hypothesis )H( 0 is accepted, i.e. the data of machines work times is

distributed exponentially with the parameters )75.38ˆ,14.43ˆ,71.48ˆ( 123 =θ=θ=θ respectively.

4.2.2. Statistical Analysis of the Reliability Functions and the Failure Rate Functions

4.2.2.1. Estimation the Reliability Function )t(R̂ Through out the relation No. (6) We got the minimum variance unbiased estimator (MVUE) of the reliability

function )t(R̂ of the three machines, a table (3) shows that:

Table 3. The Estimated Reliability Functions )t(R̂ of the machines

)t(R̂3 )t(R̂2 )t(R̂1 t 1 1 1 0

0.8167 0.7978 0.7759 10 0.6663 0.6327 0.6013 20 0.5458 0.5036 0.4654 30 0.4446 0.4005 0.3597 40 0.3618 0.3166 0.2776 50 0.2941 0.2521 0.2140 60 0.2401 0.1981 0.1647 70 0.1948 0.1568 0.1265 80 0.1580 0.1240 0.0975 90 0.1280 0.0975 0.0746 100 0.1041 0.0769 0.0570 110 0.0842 0.0606 0.0437 120 0.0680 0.0475 0.0331 130 0.0549 0.0373 0.0253 140 0.0442 0.0293 0.0193 150

It is clear throughout results of table (3) that the machine reliability R(t) of type (Twisting) is considered to be

the highest comparing thereof with reliability of type (Sewing) and type (Winder) and the reliability of type Twisting is coupled with the least failure ratio [r (t) = 0.02].

The reliability R(t) gradually decreases as long as the time of the work thereof increase, where the results show that the potentiality of work this kind of machine for (10) hours without a breakdown damage equals (0.8167)


and for (20) hours becomes (0.6663) and for of (30) hours becomes (0.5458), this till the reliability equivalent to (0.0442) where the machine work reaches (150) hour, without any failure.

The machine of (Sewing) type comes to the second rank in case of the reliability thereof, and it is followed by machine of (Winder) type to the third rank.

4.2.2.2. Estimation Failure Rate Function )t(r̂

We got the unbiased estimator with a minimum variance unbiased estimator (MVUE) of the failure rate function )t(r̂ of the three machines using the relation No.(8), shown in the table (4) as follows:

Table 4. The Estimated Failure Rate Functions )t(r̂ of the machines

No.

Machine )t(r̂

1 Winder 0.025 2 Sewing 0.023 3 Twisting 0.020

2.3. Test the Differences between the Estimative values of the Reliability Functions of the Machines

To test the differences between the estimative values of the reliability function R(t) of the machines of textile section which are to be studied, (One-way ANOVA) was used, and the results of (ANOVA) shown in the table (5) as follows:

Table 5. The result of One-way analysis of variance (ANOVA)

Sig. F Mean Square df Sum of Squares Source of Variation

0.874 0.138 0.012 2 0.024 Between Groups

0.087 45 3.936 Within Groups

- - - 47 3.960 Total

In comparing the calculated value (F) amounting to (0.138) with it's tabulated value amounting to (3.275) at the

significant level (0.05), it appeared that the calculated value is less than the tabulated value, therefore the hypothesis (H0) is accepted, which says: "There is no statistically a significance differences between the estimative values of the reliability functions R(t) of the machines of textile section which are to be studied ". 5. Conclusions and recommendations 5.1. Conclusions

1- The result of parameters estimation )ˆ( iθ of the machines work times till the occurrence of the damages mentioned in table (4) of the three machines to be studies should that the machines of type (Twisting) are the best considering its (mean time between failure), and they were of the first rank, followed by (Sewing) type in the second rank, and the (Winder) type machines in the third rank.

2- The results shows that the machine reliability )t(R̂3 type (Twisting), which is higher of (Sewing) type and

(Winder) type، which associated with the least failure rate [ ]02.0)t(r̂ = in comparison with the other failure rate of the machines from the type (Sewing), and(Winder).


3- There is no statistically a significance differences between the estimative reliability functions R(t) of the machines of textile section which are to be studied, at the significant level (0.05), with (P- value) equal to (0.874). 5.2. Recommendations

The study recommends over production organizations the necessity of running a new special administration for reliability called the (Reliability Administration) as a result of the development nature in the field of reliability, and this administration should under take to perform the following tasks:

1- Adoption of an information system for the failures of the productive machines, maintain a file on each machine and feeds through daily or weekly reports for easy review information on cases of failure of any machine with a view to their adoption in the quantitative analysis of random failures, ensuring prolongation of the useful life of the machine.

2- To define the machines and equipments specifications which would be purchased or imported from international country origin out matched by the designs and high techniques therefore which leads to the deduction of production cost and the increase of productivity from one side, and lessening the period of the machines destruction from another side.

3- Developing the work conditions of the production machines through out qualifying technical staffs of high efficiency and swing all the reserve materials necessary for the production operation duration.

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Estimation and Evaluation the Reliability of Production Machines Practical Study of the Textile Department/the National Establishment of the Jordanian Textiles in the Industrial King